Combining Texts

All the ideas for 'Set Theory', 'The Gettier Problem' and 'The Meaning of 'Meaning''

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21 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
9. Objects / D. Essence of Objects / 15. Against Essentialism
18890 Putnam smuggles essentialism about liquids into his proof that water must be H2O [Salmon,N on Putnam]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem
19699 A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]
15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality
7705 The Twin Earth theory suggests that intentionality is independent of qualia [Jacquette on Putnam]
18. Thought / C. Content / 5. Twin Earth
4099 If Twins talking about 'water' and 'XYZ' have different thoughts but identical heads, then thoughts aren't in the head [Putnam, by Crane]
12026 We say ice and steam are different forms of water, but not that they are different forms of H2O [Forbes,G on Putnam]
3208 Does 'water' mean a particular substance that was 'dubbed'? [Putnam, by Rey]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
3893 Often reference determines sense, and not (as Frege thought) vice versa [Putnam, by Scruton]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
11191 The hidden structure of a natural kind determines membership in all possible worlds [Putnam]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
11192 If causes are the essence of diseases, then disease is an example of a relational essence [Putnam, by Williams,NE]
11190 Archimedes meant by 'gold' the hidden structure or essence of the stuff [Putnam]